Cryogenic digital systems can be used in electronic systems that require voltage and current to be transferred from one temperature domain to a lower temperature domain. For example, the electronic system may include a first temperature domain at 300 Kelvin (K) and a second temperature domain at 4 K. There are other temperature domains that may be used as the second temperature domain, such as 17 K. Copper conductors are used to transfer the voltage and current between components in the temperature domains. The voltage and current on the copper conductors contribute heat into the low temperature domain using two mechanisms: a first mechanism is thermal conduction and the other mechanism is electrical heating. For example, the electronic system with a first temperature domain at 300 K and a second temperature domain at 4 K has a temperature difference (ΔT) of 296 K and the following parameters: a supply current (I0) of 1 amp supplied by a power supply over an electrical conductor pair (wire pair) with a wire length (L) of 10.0×10−2 M, with a cross-sectional area (A0) of 40 gauge wire (5.0×10−9 M2), copper resistivity (ρ0) of 1.55×10−8 Ω-M, and copper thermal conductivity (λ0) of 401 W/M-K. The logic in the second temperature domain uses 1 W of power (PL). The heat power equation for this electronic system is expressed as follows:PTOT=PL+PR+PT=PL+(2*I02*ρ0)*L/A0+(2*λ0*ΔT)*A0/L 
The cross-sectional area over the length is an aspect ratio and the length over the cross-sectional area is the inverse aspect ratio. The copper conductors are insulated on sidewalls. The PT represents the thermal conduction power and PR represents the electrical resistance power. In this example, the total power (heat) flow is 1.63 Watts (W) with 63% overhead due to PR and PT.
Heat flow to the second temperature domain in a cryogenic digital system is a concern. There is a huge efficiency factor that has to be applied to calculate the amount of energy at room temperature to pull the heat out at a low-temperature domain, as illustrated in FIG. 1.
FIG. 1 is a block diagram illustrating a cooling efficiency for removing power (heat) from a low-temperature domain in a cryogenic digital system 100. The cryogenic digital system 100 includes a room-temperature domain 104 (T2) and a low-temperature domain 102 (T0). A power supply in the room-temperature domain 104 provides power through an electrical conductor pair 106, which causes heat transfer to the low-temperature domain via thermal conduction and electrical heating. A cooling subsystem 108 is used to pull heat from the low-temperature domain. The cooling subsystem 108 has an E factor that represents the mechanical efficiency to operate the cooling subsystem (e.g., 3) and a thermodynamic efficiency (e.g., 74). The power (heat) flow into the low-temperature domain is expressed in the equation above. Using the various parameters noted above, the power (heat) flow is 1.63 W (63% overhead). The power needed in room-temperature domain 104 (T2) to remove the logic power, the thermal conduction power and the electrical resistance power is expressed in the following equation:PC20=PTOT*E*(T2/T0−1),where E is the inverse refrigerator mechanical efficiency (the inverse noted by efficiency−1) and (T2/T0−1) is the thermodynamic efficiency−1. With the values for the parameters above, the power needed (PC20) is 362 W, with 140 W due to overhead.
Optimizing heating in these cryogenic digital systems has not been a priority and thus, there have not been heating optimizations for these cryogenic digital systems.